Empirical Bayes procedures in time series regression models

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Virginia Polytechnic Institute and State University

In this dissertation empirical Bayes estimators for the coefficients in time series regression models are presented. Due to the uncontrollability of time series observations, explanatory variables in each stage do not remain unchanged. A generalization of the results of O'Bryan and Susarla is established and shown to be an extension of the results of Martz and Krutchkoff.

Alternatively, as the distribution function of sample observations is hard to obtain except asymptotically, the results of Griffin and Krutchkoff on empirical linear Bayes estimation are extended and then applied to estimating the coefficients in time series regression models. Comparisons between the performance of these two approaches are also made.

Finally, predictions in time series regression models using empirical Bayes estimators and empirical linear Bayes estimators are discussed.